##### 4.10.11 $$\left (x^2-y(x)\right ) y'(x)=4 x y(x)$$

ODE
$\left (x^2-y(x)\right ) y'(x)=4 x y(x)$ ODE Classiﬁcation

[[_homogeneous, class G], _rational, [_Abel, 2nd type, class A]]

Book solution method
Change of Variable, new dependent variable

Mathematica
cpu = 0.290493 (sec), leaf count = 232

$\left \{\left \{y(x)\to x^2 \left (1+\frac {2-2 i}{\frac {i \sqrt {2}}{\sqrt {x^2 \cosh \left (\frac {2 c_1}{9}\right )+x^2 \sinh \left (\frac {2 c_1}{9}\right )-i}}-(1-i)}\right )\right \},\left \{y(x)\to x^2 \left (1+\frac {2-2 i}{(-1+i)-\frac {i \sqrt {2}}{\sqrt {x^2 \cosh \left (\frac {2 c_1}{9}\right )+x^2 \sinh \left (\frac {2 c_1}{9}\right )-i}}}\right )\right \},\left \{y(x)\to x^2 \left (1+\frac {2-2 i}{(-1+i)-\frac {\sqrt {2}}{\sqrt {x^2 \cosh \left (\frac {2 c_1}{9}\right )+x^2 \sinh \left (\frac {2 c_1}{9}\right )+i}}}\right )\right \},\left \{y(x)\to x^2 \left (1+\frac {2-2 i}{\frac {\sqrt {2}}{\sqrt {x^2 \cosh \left (\frac {2 c_1}{9}\right )+x^2 \sinh \left (\frac {2 c_1}{9}\right )+i}}-(1-i)}\right )\right \}\right \}$

Maple
cpu = 0.182 (sec), leaf count = 53

$\left [y \left (x \right ) = \frac {\textit {\_C1} \left (\textit {\_C1} -\sqrt {\textit {\_C1}^{2}-4 x^{2}}\right )}{2}-x^{2}, y \left (x \right ) = \frac {\textit {\_C1} \left (\textit {\_C1} +\sqrt {\textit {\_C1}^{2}-4 x^{2}}\right )}{2}-x^{2}\right ]$ Mathematica raw input

DSolve[(x^2 - y[x])*y'[x] == 4*x*y[x],y[x],x]

Mathematica raw output

{{y[x] -> x^2*(1 + (2 - 2*I)/((-1 + I) + (I*Sqrt[2])/Sqrt[-I + x^2*Cosh[(2*C[1])
/9] + x^2*Sinh[(2*C[1])/9]]))}, {y[x] -> x^2*(1 + (2 - 2*I)/((-1 + I) - (I*Sqrt[
2])/Sqrt[-I + x^2*Cosh[(2*C[1])/9] + x^2*Sinh[(2*C[1])/9]]))}, {y[x] -> x^2*(1 +
 (2 - 2*I)/((-1 + I) - Sqrt[2]/Sqrt[I + x^2*Cosh[(2*C[1])/9] + x^2*Sinh[(2*C[1])
/9]]))}, {y[x] -> x^2*(1 + (2 - 2*I)/((-1 + I) + Sqrt[2]/Sqrt[I + x^2*Cosh[(2*C[
1])/9] + x^2*Sinh[(2*C[1])/9]]))}}

Maple raw input

dsolve((x^2-y(x))*diff(y(x),x) = 4*x*y(x), y(x))

Maple raw output

[y(x) = 1/2*_C1*(_C1-(_C1^2-4*x^2)^(1/2))-x^2, y(x) = 1/2*_C1*(_C1+(_C1^2-4*x^2)
^(1/2))-x^2]